This paper presents a brief introduction to the nature and different types of mathematical visualization. Some of the influences that visualization has had on the development of mathematics and its teaching are examined, in particular exploring its current status. The paper inspects the particular role visualization may have in what concerns mathematical analysis and the difficulties that surround the correct use of it, with or without the computer. Finally, a sample of exercises in visualization in basic real analysis is presented in order to show with examples its possible role in the teaching and learning of this subject. (Contains 22 references.) (Author/KHR)